Rotational Mechanical Converter (MA)

Interface (converter) between humid air and mechanical rotating networks.

blockType: AcausalFoundation.MoistAir.Elements.RotationalMechanicalConverter

Path in the library:

/Physical Modeling/Fundamental/Moist Air/Elements/Rotational Mechanical Converter (MA)

Description

The Rotational Mechanical Converter (MA) unit is the interface between the humid air network and the mechanical rotary network. The unit converts moist air pressure into mechanical torque and vice versa. It can be used as a basis for rotary actuators.

The volume of moist air in the converter changes during operation. The pressure and temperature change according to the compressibility and heat capacity of the moist air volume. Liquid water condenses out of the moist air volume when it reaches saturation.

The parameters Mechanical orientation determines whether an increase in humid air volume results in a positive or negative rotation of port R relative to port C.

Port A is the wet air port corresponding to the inverter input. Ports R and C are mechanical rotation ports corresponding to the shaft and housing, respectively.

Sub-line indices:

- properties of dry air, water vapour and impure moist air, respectively;
- water vapour at saturation;
- corresponding port;
- properties of the internal volume of moist air.

Characteristics of the modelled system:

- mass flow rate;
- energy flow rate;
- heat flow rate;
- pressure;
- density;
- universal gas constant;
- volume of moist air inside the converter;
- specific heat capacity at constant volume;
- specific enthalpy;
- specific internal energy;
- mass fraction ( - specific humidity, which is otherwise known as the mass fraction of water vapour);
- mole fraction;
- relative humidity;
- humidity coefficient;
- temperature;
- time.

The net wet air flow rates in the vessel are:

where

- condensation rate;
- is the rate of condensate energy loss;
- rate of energy addition from moisture sources and impurity gases;
and - mass flow rates of water and air through the S port.

The values and are determined by the moisture and impurity gas sources connected to the S port of the transmitter.

If the port is not used, the terms of the equation with the subscript corresponding to the port name are .

Water vapour mass conservation relates the mass flow rate of water vapour to the dynamics of the humidity level in the internal volume of humid air:

Similarly, conservation of the mass of impurity gas relates the mass flow rate of impurity gas to the dynamics of the level of impurity gas in the internal volume of humid air:

Conservation of the mixture mass relates the mass flow rate of the mixture to the dynamics of pressure, temperature and mass fractions of the internal volume of humid air:

where is the rate of change of the transducer volume.

Finally, the law of conservation of energy relates the rate of energy flow to the dynamics of pressure, temperature and mass fractions of the internal volume of moist air:

The equation of state relates the density of the mixture to pressure and temperature:

The universal gas constant of the mixture is equal to:

The volume of the converter depends on the shaft rotation:

where

- is the fluid volume at which the shaft angle of rotation is 0;
- is the volume displacement of the shaft;
- shaft rotation angle;
- mechanical orientation coefficient. If the parameters Mechanical orientation is set to , otherwise . `Pressure at A causes positive rotation of R relative to C`then , otherwise .

The shaft rotation is zero if the volume of moist air inside the inverter is . Then, depending on the value of the parameters Mechanical orientation, the following is true:

If it is set to Pressure at A causes positive rotation of R relative to C, the rotation of the interface increases when the volume of moist air increases compared to the dead volume.
If it is set to the value of. Pressure at A causes negative rotation of R relative to C, the interface rotation decreases when the wet air volume increases compared to the dead volume.

Equation describing the torque equilibrium on the transducer:

where

- is the torque from port R to port C;
- atmospheric pressure.

Gas and thermal resistances in the converter are not modelled:

When the air reaches saturation, condensation can occur. The specific humidity at saturation is:

where

- is the relative humidity at saturation (typically 1);
- water vapour saturation pressure estimated at .

The condensation rate is:

where is the value of the parameters Condensation time constant.

Condensate is subtracted from the volume of moist air as shown in the conservation equations. The energy associated with the condensate is equal to:

where is the specific enthalpy of vapour formation, estimated at .

Other amounts of moisture and impurity gas are related as follows:

Assumptions and limitations

The walls of the converter are perfectly rigid.
The gas resistance between the inlet and the interior of the transducer is negligible.
The thermal resistance between the H port and the wet air volume is not modelled.
The movable interface is lossless.
The unit does not model mechanical effects such as hard stopping, friction and inertia.

Ports

Conserving

# A — humid air inlet
humid air

Details

Humid air port, corresponds to the inverter input.

Program usage name

port

# C — hull
translational mechanics

Details

Mechanical progressive port, corresponds to the inverter housing.

Program usage name

case_flange

# R — shaft
`rotational mechanics

Details

Mechanical progressive port, corresponds to a shaft.

Program usage name

rod_flange

# H — internal temperature
`heat

Details

Heat port related to the temperature of the moist air mixture inside the converter.

Program usage name

thermal_port

# S — addition or removal of moisture and impurity gases
`moist air

Details

Connect this port to the S port of the unit from the library Moisture & Trace Gas Sources to add or remove moisture and impure gases.

Dependencies

To use this port, set the Moisture and trace gas source parameters to Controlled.

Program usage name

source_port

Output

# W — condensation rate, kg/s
scalar

Details

An output port that measures the condensation rate in the inverter.

Data types	`Float64`.
Complex numbers support	No

# F — vector signal containing data on pressure, temperature, humidity and level of impurity gases
`vector'

Details

An output port that outputs a vector signal. The vector contains the results of pressure (Pa), temperature (K), humidity level and impurity gas level measurements inside the component.

Data types	`Float64`.
Complex numbers support	No

Input

Parameters

Main

# Mechanical orientation — Select the orientation of the inverter
Pressure at A causes positive rotation of R relative to C | Pressure at A causes negative rotation of R relative to C

Details

Select the movement of the shaft in relation to the volume of moist air inside the converter:

Pressure at A causes positive rotation of R relative to C - An increase in the moist air volume results in a positive rotation of port R relative to port C.
Pressure at A causes negative rotation of R relative to C - Increase in the volume of humid air leads to a negative rotation of port R relative to port C.

Values	`Pressure at A causes positive rotation of R relative to C` \| `Pressure at A causes negative rotation of R relative to C`
Default value	`Pressure at A causes positive rotation of R relative to C`
Program usage name	`orientation`
Evaluatable	No

# Initial interface rotation — rotational displacement of port R relative to port C at the beginning of modelling
deg | rad | rev | mrad

Details

Rotational displacement of port R relative to port C at the start of the simulation. The value 0 corresponds to an initial volume of moist air equal to Dead volume.

Dependencies

To use the parameter, set the parameter Interface rotation to the value of Calculate from angular velocity of port R relative to port C:

If Mechanical orientation - Pressure at A causes positive rotation of R relative to C, then the value of the parameters must be greater than or equal to 0.
If Mechanical orientation - Pressure at A causes negative rotation of R relative to C, the value of the parameters must be less than or equal to 0.

Units	`deg` \| `rad` \| `rev` \| `mrad`
Default value	`0.0 rad`
Program usage name	`delta_phi_start`
Evaluatable	Yes

Details

Volume of moist air displaced per unit revolution of the shaft.

Units	`l/rad` \| `l/rev` \| `gal/rad` \| `gal/rev` \| `igal/rad` \| `m^3/deg` \| `m^3/rad` \| `m^3/rev` \| `cm^3/rad` \| `cm^3/rev` \| `mm^3/rad` \| `km^3/rad` \| `ft^3/rad` \| `in^3/deg` \| `in^3/rad` \| `in^3/rev` \| `Nm/Pa/rad` \| `Nm/bar/rad` \| `lbf*ft/psi/rad`
Default value	`0.01 m^3/rad`
Program usage name	`volume_displacement`
Evaluatable	Yes

# Dead volume — Humid air volume at shaft angle 0
l | gal | igal | m^3 | cm^3 | ft^3 | in^3 | km^3 | mi^3 | mm^3 | um^3 | yd^3 | N*m/Pa | N*m/bar | lbf*ft/psi | ft*lbf/psi

Details

Volume of moist air at shaft angle of rotation equal to 0.

Units	`l` \| `gal` \| `igal` \| `m^3` \| `cm^3` \| `ft^3` \| `in^3` \| `km^3` \| `mi^3` \| `mm^3` \| `um^3` \| `yd^3` \| `Nm/Pa` \| `Nm/bar` \| `lbfft/psi` \| `ftlbf/psi`
Default value	`1.e-5 m^3`
Program usage name	`dead_volume`
Evaluatable	Yes

# Cross-sectional area at port A — area normal to the flow cross-section at the inlet to the transducer
m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2

Details

The cross-sectional area of the converter inlet in the direction normal to the wet air flow path.

Units	`m^2` \| `cm^2` \| `ft^2` \| `in^2` \| `km^2` \| `mi^2` \| `mm^2` \| `um^2` \| `yd^2`
Default value	`0.01 m^2`
Program usage name	`port_area`
Evaluatable	Yes

# Environment pressure specification — method of setting the ambient pressure
Atmospheric pressure | Specified pressure

Details

Select the ambient pressure setting method:

Atmospheric pressure - atmospheric pressure is used.

Specified pressure - set the value with the parameters Environment pressure.

Values	`Atmospheric pressure` \| `Specified pressure`
Default value	`Atmospheric pressure`
Program usage name	`environment_type`
Evaluatable	No

# Environment pressure — outside pressure
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar

Details

Pressure outside the converter acting against the pressure of the moist volume of air in the converter. A value of 0 means that the gas in the converter is expanding into a vacuum.

Dependencies

To use this parameter, set the parameters Environment pressure specification to the value of Specified pressure.

Units	`Pa` \| `GPa` \| `MPa` \| `atm` \| `bar` \| `kPa` \| `ksi` \| `psi` \| `uPa` \| `kbar`
Default value	`0.101325 MPa`
Program usage name	`environment_pressure`
Evaluatable	Yes

Moisture and Trace Gas

# Relative humidity at saturation — Relative humidity above which condensation occurs

Details

Relative humidity above which condensation occurs.

Default value	`1.0`
Program usage name	`RH_saturation`
Evaluatable	Yes

# Condensation time constant — condensation time constant
d | s | hr | ms | ns | us | min

Details

A time scale factor characterising the time period for the return of the supersaturated volume of moist air to the saturation level due to condensation of excess moisture.

Units	`d` \| `s` \| `hr` \| `ms` \| `ns` \| `us` \| `min`
Default value	`0.001 s`
Program usage name	`condensation_time_constant`
Evaluatable	Yes

# Moisture and trace gas source — source of moisture and impurity gases
None | Constant | Controlled

Details

This parameter controls the usage of the S port and provides the following options for modelling moisture and impurity gas levels within the unit:

None - no impurity gas is introduced into or extracted from the block. The S port is hidden. This value is used by default.
Constant - moisture and impurity gas are introduced into or extracted from the block at a constant rate. The same parameters as in the Moisture Source (MA) and Trace Gas Source (MA) units are available in the unit settings. The S port is hidden.
Controlled - Moisture and impurity gas are introduced into or removed from the block at a time-varying rate. Port S is open. Units Moisture Source (MA) and Trace Gas Source (MA) are connected to this port.

Values	`None` \| `Constant` \| `Controlled`
Default value	`None`
Program usage name	`moisture_trace_gas_source`
Evaluatable	No

# Moisture added or removed — add or remove moisture in the form of water vapour or water
Vapor | Liquid

Details

Select whether the unit adds or removes moisture as water vapour or water:

Vapor - the enthalpy of added or removed moisture corresponds to the enthalpy of water vapour, which is greater than the enthalpy of water.
Liquid - the enthalpy of added or removed moisture corresponds to the enthalpy of water, which is less than the enthalpy of water vapour.

Dependencies

To use this parameter, set the parameter Moisture and trace gas source to . Constant.

Values	`Vapor` \| `Liquid`
Default value	`Vapor`
Program usage name	`moisture_source_phase`
Evaluatable	No

# Rate of added moisture — constant mass flow rate through the source
kg/s | N*s/m | N/(m/s) | lbf/(ft/s) | lbf/(in/s)

Details

Mass flow rate of moisture through the source.

A positive value adds moisture to the connected humid air network. A negative value removes moisture from this network.

Dependencies

To use this parameter, set the parameter Moisture and trace gas source to Constant.

Units	`kg/s` \| `N*s/m` \| `N/(m/s)` \| `lbf/(ft/s)` \| `lbf/(in/s)`
Default value	`0.0 kg/s`
Program usage name	`moisture_mass_flow`
Evaluatable	Yes

# Added moisture temperature specification — Moisture temperature setting method
Atmospheric temperature | Specified temperature

Details

Selects the method for setting the moisture temperature:

Atmospheric temperature - the atmospheric temperature set by the unit Moist Air Properties (MA), connected to the circuit, is used.
Specified temperature - the value is set with the parameters Temperature of added moisture.

Dependencies

To use this parameter, set the Moisture and trace gas source parameters to . Constant.

Values	`Atmospheric temperature` \| `Specified temperature`
Default value	`Atmospheric temperature`
Program usage name	`moisture_temperature_type`
Evaluatable	No

Details

Enter the moisture temperature. This temperature remains constant during the simulation. The unit only uses this value to estimate the specific enthalpy of added moisture. The specific enthalpy of removed moisture is determined based on the temperature of the connected humid air network.

Dependencies

To use this parameter, set the parameters Added moisture temperature specification to Specified temperature.

Units	`K` \| `degC` \| `degF` \| `degR` \| `deltaK` \| `deltadegC` \| `deltadegF` \| `deltadegR`
Default value	`293.15 K`
Program usage name	`moisture_temperature`
Evaluatable	Yes

# Rate of added trace gas — constant mass flow rate through the source
kg/s | N*s/m | N/(m/s) | lbf/(ft/s) | lbf/(in/s)

Details

Reflects the mass flow rate of impurity gas through the source. A positive value adds impurity gas to the connected humid air volume, a negative value removes it.

Dependencies

To use this parameter, set the Moisture and trace gas source parameters to . Constant.

Units	`kg/s` \| `N*s/m` \| `N/(m/s)` \| `lbf/(ft/s)` \| `lbf/(in/s)`
Default value	`0.0 kg/s`
Program usage name	`trace_gas_mass_flow`
Evaluatable	Yes

# Added trace gas temperature specification — method for setting the impurity gas temperature
Atmospheric temperature | Specified temperature

Details

Selection of the impurity gas temperature setting method:

Atmospheric temperature - the atmospheric temperature set by the Moist Air Properties (MA) unit connected to the mains is used.
Specified temperature - the value is set with the parameters Temperature of added trace gas.

Dependencies

To use this parameter, set the Moisture and trace gas source parameters to . Constant.

Values	`Atmospheric temperature` \| `Specified temperature`
Default value	`Atmospheric temperature`
Program usage name	`trace_gas_temperature_type`
Evaluatable	No

Details

Enter the desired temperature of the impurity gas to be added. This temperature remains constant during the simulation. The unit only uses this value to estimate the specific enthalpy of the added impurity gas. The specific enthalpy of the removed impurity gas is determined based on the temperature of the connected wet air volume.

Dependencies

To use this parameter, set the parameters Added trace gas temperature specification to . Specified temperature.

Units	`K` \| `degC` \| `degF` \| `degR` \| `deltaK` \| `deltadegC` \| `deltadegF` \| `deltadegR`
Default value	`293.15 K`
Program usage name	`trace_gas_temperature`
Evaluatable	Yes